## Monday, April 10, 2006

### Two cups

You have two cups, one containing orange juice and one containing and equal amount of lemonade. One teaspoon of the orange juice is taken and mixed with the lemonade. Then a teaspoon of this mixture is mixed back into the orange juice. Is there more lemonade in the orange juice or more orange juice in the lemonade?

1. I think there is more lemonade in the orange juice since it went in as a pure teaspoon

2. I would agree, the teraspoon of lemonade going into the OJ isn't a pure mixture.

3. There's the same amount of lemonade in the orange juice as orange juice in the lemonade. Each cup ends with the same volume of liquid that it started with, and there's still an equal amount of each juice between the two cups.

But I could be wrong! ;-)

4. I made each one 10 teaspoons for example:

When I move a Teaspoon of OJ to LA:

OJ= 9x
LA= 1x + 10y =11 tspn total volume

When I take one back over to the lemonade I am taking 1/11th of each over after mixing them VERY thorougly

Thus I have:

OJ= 9 1/11x + 10/11y
LA= 9 1/11y + 10/11x

So yeah, after doing it i figured it out. I musta missed few 11ths somewhere

5. Karnov... can you explain the 1/11 th aspect to me??

6. I have a similar problem to figure out but start off with 8 ounces of juice?
Not understanding the 1/11 th fractional part.

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